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These show, that if p has the value 1 (for "true") and q has the value 0 (for "false"), then the expression p&&q will have the value 0 and the expression p | | q will have the value 1. Example 2.6 the Maximum of Three Again The same problem as Ex. 2.4 using compound conditionals: int a, b, c; cout <<"Enter three integers: "; cin >>a >>b >>c; if (a>=b && a>=c) cout <<a <<endl; if (b>=a && b>=c) cout <<b <<endl; if (c>=a && c>=b) cout <<c <<endl; Note that Ex. 2.6 is no improvement over Ex. 2.4. Its purpose is simply to illustrate the use of compound conditionals. Here is another example using a compound conditional: Example 2.7 User-Friendly Input This program allows the user to input either a Y or a y for "yes": char ans; cout <<"Are you enrolled (y/n): "; cin >>ans; if (ans=='Y' | | ans=='y') cout <<"Enrolled.\n"; else cout <<"Not enrolled.\n";
Are you enrolled N Not enrolled.
It prompts the user for an answer, suggesting a response of either y or n. Then it accepts any character and concludes that the user meant "no" unless either a Y or a y is input. Compound conditionals using && and || do not evaluate the second part of the conditional unless necessary. This is called short-circuiting or lazy evaluation. As the truth tables show, (p&&q) will be false if p is false. So there is no need to evaluate q if p is false. Similarly, if p is true, then there is no need to evaluate q to determine that (p||g) is true. The value of short-circuiting is shown in the following example: Example 2.8 Short-Circuiting in a Condition This fragment tests integer divisibility: int n, d; cout <<"Enter two positive ints: "; cin >>n >>d; if (d>O&&n%d==O) cout <<d <<" divides " <<n <<endl; else cout <<d <<" does not divide" <<n <<endl;
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Enter two positive ints: 300 6 6 divides 300
Enter two positive ints: 300 7 7 does not divide 300
Enter two positive ints: 300 0 0 does not divide 300
In the first run, d is positive and n%d is zero, so the compound condition is true. In the second run. d is positive but n%d is not zero, so the compound condition is false. In the third run, d is zero, so the compound condition is determined to be false without evaluating the second component "n%d==0". This short-circuiting prevents the program from crashing because when d is zero the expression n%od cannot be evaluated. Boolean Expressions A Boolean expression is a condition that is either true or false. The expressions d>0, n%d==0, and (d>0 && n% d==0) are Boolean expressions. As we have seen, Boolean expressions evaluate to integer values where 0 means "false" and every nonzero value means "true." Since all nonzero integer values are interpreted as meaning "true," Boolean expressions are often disguised. For example, the statement if (n%d) cout <<"n is not a multiple of d"; will print precisely when n% d is not zero. That happens when d does not divide n evenly, because n%d is the remainder from the integer division. Boolean expressions having integer values can lead to some surprising anomalies in C++. For example, the following line might be written by a novice C++ programmer: if (x >= y >= z) cout <<"max = x"; Obviously, the programmer intended to write if (x >= y && y >= z) cout <<"max x"; // OK //ERROR!
The problem is that the erroneous line is syntactically correct, so the compiler will not catch the error. In fact, the program could run without any apparent error at all. This is a run-time error of the worst kind because there is no clear indication that anything is wrong. The source of the difficulty described here is the fact that Boolean expressions have numeric values. Suppose that x and y both have the value 0 and that z has the value 1. The expression (x>=y>=z) is evalu-
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